The dismissed possession charge itself won't interfere with your ability to get your CCW. However, the manner in which the case is recorded in the computer system may cause a "hiccup in the giddyup". I'm not sure how it works in Florida - someone may see "no information/not available" and know immediately that it means that the charge was dismissed. Or they might think that the case is still pending, or that you were convicted and the database entry was never updated.

But I'd go ahead and try and see what happens. Since the charge was dismissed, it's not as if you're a prohibited person who's trying to fraudulently obtain a CCW. At worst, you're just the victim of a clerical error.